本篇研究使用拉普拉斯轉換(Laplace transform)和有限差分法(finite difference method)來評價雙邊障礙信用價差選擇權(double-barrier credit spread option)。傳統的顯然有限差分法(Explicit Finite difference)雖簡單易懂，卻存在穩定性(Stability)的問題，卽較難收歛至精確的數值解(numerical solution);隱然有限差分法(Implicit finite difference)雖會收歛到精確數值解，但當我們將時間變數間距(Time step)縮小時，其計算過程卻相當耗時。使用上述組合型方法(Hybrid method)的優點在於經過拉普拉斯轉換之後，排除了時間變數，因此，傳統之有限差分法運算耗時及不易收歛到精確數值解的問題都可獲得改善。本篇研究將以此組合型方法所求得轉換後之數值解，經由數值逆拉普拉斯轉換(numerical inversion of Laplace transform)後，即可求得在原來時間領域(Time domain)下任ㄧ時點的選擇權價格，整個計算的過程將更快速且穩定。

This paper uses the combination of the Laplace transformation and the finite difference method to value the double-barrier credit spread option. The major advantage of the combination method over the finite difference method is that the Laplace transformation will eliminate the time steps, thus, an accurate and precise numerical solution will be obtained quickly. The hybrid method can provide practitioners with a more efficient and applicable way to solve the PDE (partial differential equation) within various boundary constraints. Therefore, the method will be a highly powerful approach to price exotic options with complex features.

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